# Polarization-dependent and Valley-protected Lamb Waves in Asymmetric Pillared Phononic Crystals

## TL;DR

This paper demonstrates topologically protected polarization-dependent Lamb wave propagation in asymmetric phononic crystals, revealing unidirectional transport and valley protection, with implications for robust waveguiding in elastic media.

## Contribution

It introduces a novel design of asymmetric pillared phononic crystals enabling valley-protected Lamb waves with tunable topological phases and polarization-dependent transport.

## Key findings

- Realization of valley-protected Lamb waves at domain walls.
- Observation of unidirectional wave transport with minimal reflection.
- Topological phase transition controlled by symmetry-breaking perturbations.

## Abstract

We present the realization of the topological valley-protected zero-order antisymmetric (A0) or symmetric (S0) and zero-order shear-horizontal (SH0) Lamb waves at different domain walls based on topologically distinct asymmetric double-sided pillared phononic crystals. The elastic periodic structures have either the triangular or the honeycomb symmetry and give rise to a double-negative branch in the dispersion curves. By artificially folding the doubly negative branch, a degenerate Dirac cone is achieved. Different polarization-dependent propagation along the same primary direction along the constituent branches are presented. Moreover, divergent polarization-dependent phenomena along different primary directions along a given branch are also reported. By imposing two large space-inversion symmetry (SIS) breaking perturbations the topological phase transition is obtained. We show that the Berry curvature becomes strongly anisotropic when the wave vector gets away from the valleys. Further, we demonstrate the unidirectional transport of A0, S0, and SH0 Lamb waves at different domain walls in straight or Z-shape wave guides. In the large SIS breaking case, we show negligible reflection at the zigzag outlet of the straight wave guide and occurrence of weak inter-valley scattering at the bending corners of the Z-shape wave guide. For a larger strength of SIS breaking, the edge states are gapped and strong reflection at the zigzag outlet and bending corners is observed. The topological protection cannot be guaranteed any more in that case.

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Source: https://tomesphere.com/paper/1907.11127